The number of active antenna elements in an antenna array is increasing over time as may be observed by recent releases of Long Term Evolution (LTE) system where the newer releases support Multiple-Input Multiple-Output (MIMO) links with an increasing amount of antennas. Further increase in number of antenna elements, particularly at the base stations, is envisioned as an attractive physical-layer solution to improve the spectral efficiency of future communication systems such as fifth generation (5G) systems and in response to ever-increasing data traffic. So the term Massive MIMO (mMIMO) is employed to refer to the cases where the receivers and/or the transmitters enjoy many active antenna elements, such as e.g. hundreds of antenna elements. These types of mMIMO antenna systems are also known as Large-Scale Antenna Systems, Very Large MIMO, Hyper MIMO, Full-Dimension MIMO, Many-Antenna Base Stations and/or ARGOS.
To enable Space-Division Multiple-Access (SDMA) with mMIMO, the channel matrix between transmit antennas and receive antennas should be known. The channel estimation is an essential part as it allows separating the data streams associated with different User Equipments (UEs), served by the base station. In fact, one can view the channel matrix/vectors for example between different UEs and the base station as a spatial signature generated by the environment where one needs to learn such a random set of spatial signatures. Having learned the so-called spatial signatures, one can then try to perform spatial filtering (e.g. projection of the received baseband signals in the signal space spanned by the estimated channel vectors) at the receiver or spatial pre-coding (e.g. transmission of the data sequences in a properly chosen subspace of the signal space spanned by the estimated channel matrix) at the transmitter to ensure concurrent transmission and reception of multiple UEs with a negligible or no inter-user interference.
To estimate the channel between different nodes in a wireless communication network, i.e. UEs, base station/network node, access node, radio head, hyper transmitters, etc., one generally transmits pilot sequences known both by the transmitter and the receiver. These known pilot sequences are also referred to as reference signals/symbols or pilot signals/symbols. These expressions may sometimes be used alternatively for denoting the same thing as pilot sequences. Using these pilot sequences, the unknown radio channel between transmit and receive nodes may be estimated. Sending the pilot sequences in general leads to a loss in spectrally efficiency as it requires additional time-frequency resources to be used. The number and density of pilot sequences respectively depends on the number of antennas and time-frequency characteristics of the channel.
To learn the channel (e.g., the equivalent complex number affecting the transmitted signals for narrowband radio channels), at least one linear equation per number of unknowns is needed to find a meaningful estimation of the channel in general and in particular when the antenna spacing are configured such that it results to a full rank channel matrix. So to learn for example a downlink channel from a base station with nt antennas to K users each with nr antennas, at least nt pilots signal are needed; i.e. one pilot per antenna, or alternatively nt orthogonal sequences of length nt (or spanning a subspace with dimension nt) are required. For uplink transmission, however the required number of pilot sequences changes to Knr. It may be noted that the number of pilot sequences increases linearly with the number of antennas and hence it does not scale favourably for massive antenna arrays.
A remedy to this shortcoming is to use the channel reciprocity. That is when the uplink and downlink transmissions occur over the same frequency band the uplink and downlink channel remains the same at a given time instant. So the Time-Division Duplex (TDD) operation allows using the number of pilot sequences according to:min{Knr,nt}  (1)
In practice, the typical number of antennas at a User Equipment (UE), such as e.g. a mobile telephone, a computer tablet, a laptop with wireless capability or similar portable device, is kept low to allow smaller size, simpler processing for a longer battery life time and cheaper UE. However the base station may afford a larger number of antennas, where nr<<nt. So for example for a scenario with massive MIMO at the base station and K UEs each with a single antenna the required number of pilot sequences in order to learn the uplink and downlink channel in TDD mode is equal to the number of UEs. For massive MIMO, it is expected to have K<<nt, which results in an affordable overhead associated to the pilot sequences.
The density of the pilot sequences depends on the radio channel characteristic. The characteristics of the radio channel change over time and frequency. However the variations in time depend on the mobility of the UEs. The faster the UEs move, the faster the channel in time changes due to a larger Doppler frequency. The radio channel can be assumed unchanged within the coherence time Tc, which is a function of the carrier frequency and the velocity of the UEs. So to learn the channel between transmit and receive antennas over a coherence time, at least one pilot symbol per coherence time is needed. Similarly, the radio channel varies in frequency. However the changes in the frequency are generally characterised by the coherence bandwidth, Bc, which depends on the delay profile of the channel and the symbol duration.
To sum-up, in order to learn the radio channel in the time-frequency grid in the TDD mode for mMIMO communication in a cell with K UEs each with a single antenna, K orthogonal pilot sequences, each associated to a UE, are required over a time-frequency grid of the size Tc×Bc.
FIG. 1A depicts a conventional transmission frame structure for Time-Division Duplex (TDD) communications where each frame is consisted of multiple subframes. In FIG. 1A, there are L subframes. Each subframe comprises pilot data, for channel estimation, control signals for uplink and downlink transmission and then the data transmission. Each subframe is a grid of Resource Elements (REs) over time and frequency, where each resource element consumes one symbol duration and one subcarrier. The guard intervals may also be situated between uplink and downlink transmissions as well as between the pilot region and data region, which however for simplicity of exposition have been omitted.
Non-orthogonal multiple-access is the paradigm to concurrently schedule multiple UEs over the same time-frequency resource element. One appealing approach to separate the uplink superimposed data streams may be to use spatial domain provided by a plurality of antennas. Toward this end, the receiver needs to estimate the channels from each UE and then using the estimated channels to perform spatial filtering to remove the cross-talk, i.e. interference, among the superimposed streams.
FIG. 1B illustrates the uplink transmission for K UEs over shared time-frequency resource elements where each frame has two regions: pilot region and data region which also comprises the control data.
To overcome the pilot contamination, it is required to ensure the pilot sequences transmitted in the time-frequency grid dedicated to the pilot transmissions are orthogonal to one another. One example of orthogonal pilot transmission is illustrated in FIG. 1C. The conventional solution is to schedule multiple UEs where the total number of UEs in the cell is less than the total number of orthogonal sequences. FIG. 1C depicts the one example for orthogonal pilot transmission obtained by Time-Division Multiplexing (TDM) in the pilot region, and non-orthogonal data transmission over shared uplink resources. It is understood that in the pilot region one may use Frequency-Division Multiplexing (FDM) or a combination of FDM and TDM. For uplink transmission however, the UEs may employ the pilot sequences over the entire sub-band, for which TDM or Code-Division Multiplexing (CDM) over pilot may be used, such as pilots with covering code used in LTE.
However, the maximum number of orthogonal sequences that may be placed in the pilot time-frequency grid is limited. This consequently puts a limit on the number of scheduled UEs regardless of the number of antennas. So the prior art is incapable to allow UE scheduling beyond half of the coherence time and also leads to intra-cell (for pilot sequence reuse within a cell) or inter-cell interference for reused pilot sequences across different cells.
For TDD mMIMO communications when the number of antennas is very large, the limiting factor for achieving high network throughput is the limited number of orthogonal pilot sequences. For radio channels with the coherence time Tc symbols, for high number of antennas, in order to maximise the aggregate throughput, it is optimal to allocate half of the coherence time for channel training, i.e. transmitting pilot or reference sequences. Therefore, the conventional solution is designed to schedule up to:
                    K        =                  ⌊                                    T              c                        2                    ⌋                                    (        2        )            
UEs within each coherence interval. For multi-carrier systems:
      K    =          ⌊                                    B            c                    ⁢                      T            c                          2            ⌋        ,where Bc denotes the coherence bandwidth. In general, it is desirable to schedule more users; i.e., provide service to as many as UEs as the number nodes that require connection are increasing over time. However, the higher number of active UEs leads to higher interference among UEs and hence it is not clear how the aggregate rate will affected. In particular, for mMIMO, scheduling more UEs beyond that in equation (2), leads to the pilot contamination which causes severe degradations in the performance. To illustrate the pilot contamination phenomena; consider two UEs that transmit the same pilot symbol followed by data symbol sequences over shared uplink. Then the access node receives the signal:yp=h1xp+h2xp+zp,  (3)wherein yp denotes the received noisy signal vector of dimension nt×1, xp denotes the transmitted pilot symbol from both UEs (i.e. pilot reuse), hi denotes the channel vector between UE i and the antenna array at the access node, which has the dimension nt×1, and zp denotes Average White Gaussian Noise (AWGN), which has the dimension n×1.
Then, using minimum mean-square error (MMSE) channel estimation, the estimated channel will be:ĥ=h1+h2+ze,  (4)where ze denotes channel estimation error.
The received noisy superimposed data may then be written as:yd=h1xd1+h2xd2+zd,  (5)where yd denotes the received noisy signal vector of dimension nt×1, xdi denotes the transmitted data symbol from UE i, hi denotes the channel vector between UE i and the receiver, which has the dimension nt×1, and zd denotes AWGN, which has the dimension nt×1. The access node then performs spatial filtering to separate the data stream for the first UE. For a very large array, i.e. nt>>1, the Matched Filtering (MF), a.k.a. Maximum-Ratio Combining (MRC) is optimal and the following rate is achievable:
                              R          =                      log            ⁡                          (                              1                +                                                      P                    1                                                        P                    2                                                              )                                      ,                            (        6        )            where independent and identically distributed (i.i.d.) Rayleigh fading with unit variance is assumed and the average transmit power of each user is set to Pi. From equation (6), it is seen that large antenna arrays under pilot contamination helps to remove the noise and small-scale fading but the inter-user interference remains. Thus for P1=P2, R=0.5 [bit/s/Hz] at maximum is achievable. The actual rate by accounting the pilot overhead will be even less. Therefore pilot reuse causes significant rate-loss in spite of the fact that there exist many active antenna elements.
Semi-Orthogonal Multiple-Access (SOMA) is a solution constructed in a way that it enables to schedule twice as many UEs in each coherence interval as compared to the conventional TDD yet avoiding the pilot contamination. The construction of SOMA is in a way that it possesses a semi-orthogonal feature in signal transmission such that in a given time slot some users appear orthogonal while the remaining users may transmit non-orthogonally. The main shortcoming of SOMA is that the channels of the UEs cannot be estimated simultaneously without interference. However, by sequential decoding the interference-free sequential channel estimation becomes feasible. Thus, having estimated the first channel vector only matched filtering for spatial filtering can be employed since the other channels are unknown. Matched Filtering is optimal for very large arrays, however for smaller size arrays, other spatial filtering such as zero-forcing (ZF) and MMSE processing can outperform that with Matched Filtering.
It appears that further development is required in order to be able to schedule more UEs in a network by a network node to provide higher aggregate rates, in particular in a massive MIMO environment where intense pilot signalling is required.